Combinatorics, Algebra, & Topology Seminar
Fall 2020
All talks are on google Meet at the specific Meet address.

Nov09

The geometry of parabolic Hamiltonian reductionMee Seong ImUSNATime: 03:45 PM
View Abstract
n the construction of Hamiltonian reductions in symplectic geometry, rich connections to Hilbert schemes, CalogeroMoser spaces, and rational spherical Cherednik algebras have emerged. A parabolic analogue of the classical general linear group construction (realized after a reduction from the cotangent bundle of enhanced partial GrothendieckSpringer resolutions) potentially opens doors for its connections to isospectral Hilbert schemes, partial flag Hilbert schemes, and other algebraic varieties that are important in geometric representation theory, algebraic combinatorics, and quantum topology. Our construction can also be realized by certain (partial) quiver flag varieties, appearing in the geometric interplay in quiver Hecke algebras that categorify quantum groups. I will discuss a parabolic analogue of the cotangent bundle of the extended general linear Lie algebra, discussing the complete intersection of the zero fiber of a moment map, an enumeration of the irreducible components, and a parabolic analog of an almostcommuting scheme appearing in the study of CalogeroMoser systems. I will end with conjectures on their birationality of their geometric invariant theory (GIT) quotient, which depends on the stability condition, to wellknown Hilbert schemes.